Limits and End Behavior - All

When we evaluate limits of a function as (x) goes to infinity or minus infinity, we are examining something called the end behavior of a limit. In order to determine the end behavior, we need to substitute a series of values or simply the function determine what number the function approaches as the range of the function increases or decreases towards infinity or minus infinity.

Sample Problems
(3)

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Problem 1

Observing end behavior, how to find the limit of a rational function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.

Problem 2

How to evaluate the limit of an exponential function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph to determine end behavior.

Problem 3

How to determine the oblique asymptote of the graph of a rational function to determine end behavior.